Mathematical modeling of Earth's dynamical systems
Subtitle: a primer
By: Rudy Slingerland and Lee Kump
Contributors: Kump, Lee R.
Publisher: Princeton University Press
Published: 2011
Place of publication: Princeton, N.J
Language: eng
Number of pages: 231
ISBN-13: 9780691145136; 9780691145143
Subjects: Mathematical models; Gaia hypothesis
Notes: Includes bibliographical references (p. 211-215) and index.
Table of contents: title: Machine generated contents note: -- 1.; title: Modeling and Mathematical Concepts --; title: Pros and Cons of Dynamical Models --; title: An Important Modeling Assumption --; title: Some Examples -- -- Example I; title: Simulation of Chicxulub Impact and Its Consequences -- -- Example II; title: Storm Surge of Hurricane Ivan in Escambia Bay --; title: Steps in Model Building --; title: Basic Definitions and Concepts --; title: Nondimensionalization --; title: A Brief Mathematical Review --; title: Summary -- -- 2.; title: Basics of Numerical Solutions by Finite Difference --; title: First Some Matrix Algebra --; title: Solution of Linear Systems of Algebraic Equations --; title: General Finite Difference Approach --; title: Discretization --; title: Obtaining Difference Operators by Taylor Series --; title: Explicit Schemes --; title: Implicit Schemes --; title: How Good Is My Finite Difference Scheme? --; title: Stability Is Not Accuracy --; title: Summary --; title: Modeling Exercises -- -- 3.; title: Box Modeling: Unsteady, Uniform Conservation of Mass --; title: Translations; title: Example I; title: Radiocarbon Content of the Biosphere as a One-Box Model -- -- Example II; title: The Carbon Cycle as a Multibox Model -- -- Example III; title: One-Dimensional Energy Balance Climate Model --; title: Finite Difference Solutions of Box Models --; title: The Forward Euler Method --; title: Predictor-Corrector Methods --; title: Stiff Systems -- -- Example IV; title: Rothman Ocean --; title: Backward Euler Method --; title: Model Enhancements --; title: Summary --; title: Modeling Exercises -- -- 4.; title: One-Dimensional Diffusion Problems --; title: Translations -- -- Example I; title: Dissolved Species in a Homogeneous Aquifer -- -- Example II; title: Evolution of a Sandy Coastline -- -- Example III; title: Diffusion of Momentum --; title: Finite Difference Solutions to 1-D Diffusion Problems --; title: Summary --; title: Modeling Exercises -- -- 5.; title: Multidimensional Diffusion Problems --; title: Translations -- -- Example I; title: Landscape Evolution as a 2-D Diffusion Problem -- -- Example II; title: Pollutant Transport in a Confined Aquifer -- -- Example III; title: Thermal Considerations in Radioactive Waste Disposal; title: Finite Difference Solutions to Parabolic PDEs and Elliptic Boundary Value Problems --; title: An Explicit Scheme --; title: Implicit Schemes --; title: Case of Variable Coefficients --; title: Summary --; title: Modeling Exercises -- -- 6.; title: Advection-Dominated Problems --; title: Translations -- -- Example I; title: A Dissolved Species in a River -- -- Example II; title: Lahars Flowing along Simple Channels --; title: Finite Difference Solution Schemes to the Linear Advection Equation --; title: Summary --; title: Modeling Exercises -- -- 7.; title: Advection and Diffusion (Transport) Problems --; title: Translations -- -- Example I; title: A Generic 1-D Case -- -- Example II; title: Transport of Suspended Sediment in a Stream -- -- Example III; title: Sedimentary Diagenesis: Influence of Burrows --; title: Finite Difference Solutions to the Transport Equation --; title: QUICK Scheme --; title: QUICKEST Scheme --; title: Summary --; title: Modeling Exercises -- -- 8.; title: Transport Problems with a Twist: The Transport of Momentum --; title: Translations -- -- Example I; title: One-Dimensional Transport of Momentum in a Newtonian Fluid (Burgers' Equation); title: An Analytic Solution to Burgers' Equation --; title: Finite Difference Scheme for Burgers' Equation --; title: Solution Scheme Accuracy --; title: Diffusive Momentum Transport in Turbulent Flows --; title: Adding Sources and Sinks of Momentum: The General Law of Motion --; title: Summary --; title: Modeling Exercises -- -- 9.; title: Systems of One-Dimensional Nonlinear Partial Differential Equations --; title: Translations -- -- Example I; title: Gradually Varied Flow in an Open Channel --; title: Finite Difference Solution Schemes for Equation Sets --; title: Explicit FTCS Scheme on a Staggered Mesh --; title: Four-Point Implicit Scheme --; title: The Dam-Break Problem: An Example --; title: Summary --; title: Modeling Exercises -- -- 10.; title: Two-Dimensional Nonlinear Hyperbolic Systems --; title: Translations -- -- Example I; title: The Circulation of Lakes, Estuaries, and the Coastal Ocean --; title: An Explicit Solution Scheme for 2-D Vertically Integrated Geophysical Flows --; title: Lake Ontario Wind-Driven Circulation: An Example --; title: Summary --; title: Modeling Exercises.